Development Length and Lateral Spacing Requirements of Prestressing Strand for Prestressed Concrete Bridge Girders

70

J. Harold Deatherage Ph.D., P.E. Associate Professor of Civil Engineering University of Tennessee Knoxville , Tennessee

Edwin G. Burdette Ph.D., P.E.

Professor of Civil Engineering University of Tennessee

Knoxville, Tennessee

Chong Key Chew, Ph.D. Structural Engineer Malaysia (Formerly, doctoral student at University of Tennessee Knoxville , Tennessee)

To respond to an FHWA memorandum re­stricting the use of certain sizes of seven-wire strand in prestressed concrete girders, the PC/ sponsored a research program at the University of Tennessee at Knoxville. Twenty full-scale AASHTO Type I beams with various strand diameters were statically tested to fail­ure. Transfer and development lengths for !6 in. (13 mm), !6 in. special (13.3 mm), Yte in. (14 mm) and 0.6 in. (15 mm) diameter strands were determined. Also, minimum strand spac­ing was investigated for !6 in. (13 mm) diame­ter strand. Factors that affect both transfer and development length are evaluated and discussed. Based on the test data, equations for transfer and developemnt length of strand are proposed. The computed and measured moment capacities of the girder sections are compared and reasons for variations are ex­plained. It is concluded that the use of 0.6 in. (15 mm) diameter strand should be accepted as standard practice and a center-to-center spacing of 1.75 in. (44.5 mm) should be al­lowed for !6 in. (13 mm) diameter strand.

I n a memorandum dated October 26, 1988, the Federal Highway Administration (FHW A) imposed several re­strictions on the use of seven-wire prestressing strand in

prestressed concrete girders . Criteria were established for minimum strand spacing and for development length re­quirements of prestressing strand with vary ing diameters.

PCI JOURNAL

These restrictions stemmed primarily from the results of some research re­ported in Ref. 1.

Specifically, the FHWA restrictions were as follows:

1. The use of 0.6 in. (15 mm) diam­eter strand would be prohibited.

2. Minimum center-to-center strand spacing would be four times the nomi­nal strand diameter.

3. Development length for all strand sizes would be 1.6 times the value ob­tained from AASHTO Eq. (9-32).

4. Where the strand is debonded (blanketed), the development length would be 2.0 times the value obtained from AASHTO Eq. (9-32).

These restrictions placed severe bur­dens on producers of precast, pre­stressed concrete bridge members. In several cases, projects had to be re­designed or alternate materials were selected for construction. Conse­quently , the Precast/Prestressed Con­crete Institute (PCI) undertook a re­search program to generate additional data for comparison with the findings reported in Ref. 1.

In April 1989, an experimental re­search project was initiated at the Uni­versity of Tennessee at Knoxville (UTK) to investigate the transfer and development length of 270 ksi (1860 MPa), low-relaxation seven-wire pre­stressing strand for prestressed con­crete girders. This research project, which primarily involved fabrication and testing of 20 full-scale AASHTO Type I prestressed concrete bridge beams, was completed in November 1989.

RESEARCH OBJECTIVES Transfer and development lengths

for ~ in. (13 mrn) , ~ in. special (13.3 mm) , Y,6 in . (14 mm) and 0.6 in. (15 mm) diameter strands were deter­mined. Care was taken to fabricate the specimens in accordance with stan­dard industry practice and, at the same time, to use the practices which are considered most likely to influence the transfer and development lengths of strand.

For example, each of the specimens was detensioned using flame cutting rather than gradual detensioning. Also, strand was protected as much as possi-

January-February 1994

12"

~---+--+-+--.......

16" .I 2@s

~ 1

AREA = 276 SQ.IN. (.178 ffi2) 4

= 22750 IN. (946,926 em~

Cb = 12.59 IN. (320 mm)

dp:

d'p

Depth to the centroid of bottom prestressed steel strand

Depth to the centroid of top prestressed steel strand

s : strand spacing, in.

To convert from inches to mm, multiply by 25.4.

dia (in .} c (in. ) 0.5" 2.0" 0.525" 2.0" 9/ 16" 2.0" 0.6" 2.5"

Fig. 1. AASHTO Type I beam cross section. Strand pattern and strand spacing.

ble to ensure that "mill conditions" would be simulated; i.e ., weathering would not be a factor in the analysis.

Several specimens were evaluated using Y, in. ( 13 mm) diameter strand provided by various strand suppliers. Comparisons were made to determine whether the manufacturing process in­fluences transfer and development lengths. The effect of reducing the strand spacing from 4.0 diameters to 3.5 was also studied.

LITERATURE REVIEW Since 1950, much research has been

reported on the transfer and develop­ment lengths of seven-wire prestress­ing strand. An extensive review of this literature is presented in the final re­port on the research reported in this paper. 2 Unfortunately, no analytical model has evolved from this research which can satisfactorily predict the bond development characteristics of prestressing strand. This inability to analytically predict the behavior of strand within its development length places a particularly high premium on

test results which purport to provide some definition of transfer and devel­opment lengths and to identify and quantify some of the variables affect­ing them.

In 1954, Janney 3 explained the mechanism of bond between prestress­ing steel and concrete as consisting of adhesion, friction and mechanical re­sistance. This work was followed by considerable other research ,<·8 notably that by Hanson and Kaar,' which led to the Aroerican Association of State Highway and Transportation Officials (AASHTO) and American Concrete Institute (ACI) Code requirements which have been in use for over a decade. Then , a s tudy reported by Cousins, Johnston and Zia' raised seri­ous questions about the validity of the AASHTO/ACI equation for strand de­velopment length and led to the FHW A memorandum of October 26, 1988.

The uncertainty created in the pre­stressed concrete industry by the 1988 FHW A memorandum led to the initia­tion of several research projects,9

•10 in­

cluding the one reported herein.2 The

71

End of Beam

#5 Shear ( SR) Reinforcement

24"

16 double SR

6"

~ " --- 14 spaces @ 6" o.c.

l I l II r I 1 l . l ~ 1 ,l

z·l 9 spaces @ 4" o.c. ~10 double CR_.

~

To convert from inches to mm, multiply by 25.4

<

Fig. 2. Shear and confinement reinforcement in each end of beam.

Pattern "A"

• •

• • ••• • • •

Pattern"B"

Fig. 3. Strand configuration for Patterns A, B and C.

72

•

• •• • •• Pattern "C"

work reported here, performed at the University of Tennessee in 1989, gen­erated data which shed further light on the prediction of transfer and develop­ment lengths of prestressing strand.

SPECIMEN DESIGN AND DESIGNATION

All beams were 31 ft (9.45 m) long, designed to be sufficient in length for two development length tests on each beam. The beam specimens were de­signed so that each end of the beams provided for a set of strand end-slip measurements, a set of transfer length data and a development length test. Fig. 1 shows the cross-sectional prop­erties and dimensions of the beams. Fig. 2 shows the details of shear and confinement reinforcement used in all beams. These detail s are typical of those used by the Tennessee Depart­ment of Transportation (TDOT).

Sixteen beams divided into four groups utilized strands from Florida Wire and Cable Co. (FWC) at a strand spacing of 2 in. (51 mm). Four beams in each of the four groups with 2 in. (51 mm) strand spacing were pre­stressed with strands of ~ in. (13 mm), ~ in. special (13 .3 mm), 7'16 in. (14 mm) or 0.6 in. (15 mm) in diameter. The re­maining four beams in a strand manu­facturer's group had 1.75 in. (44.5 mm) strand spacing, and each was pre­stressed with Yz in. (13 mm), 270 ksi (1860 MPa), low-relaxation strand from one of the following manufac­turers: Shinko Wire America Inc. (SW AI), Union Wire Rope (UWR), FWC or American Spring Wire Corp . (ASW) .

The initial prestress in all strands of the test beams was designed to be 203 ksi (1400 MPa), or 75 percent of the specified ultimate strength of the strands . Elongation measurements were used in the field to obtain this stress. The number of prestressi ng strands used in a beam varied with the size of the strands. Fig. 3 shows the various strand configurations used.

All strands were received encased in moisture-proof wrapping and appeared to be free of rust. These strands were shiny when prestressing was applied. The surface condition of these strands is labeled as "Milled." However, sev-

PCI JOURNAL

Table 1. Summary of beam properties.

Specimen Strand Strand Strand Depth of steel, in. Steel area, sq in.

designation I surface pattern spacing, in. Bottom Top Bottom Top

5-1 -EXT MILLED I B

5- 1-INT MILLED B

5-2-EXT MILLED I

B

5-2-INT MILLED B

5-3-EXT W-I DAY B

5-3-INT W-I DAY

I

B

5-4-EXT W-I DAY B

5-4-!NT W-LDAY B

S-SW AI-EAST W-3 DAYS

I

B

5-SWAJ-WEST W-3 DAYS B

5-UWR-EAST W-3 DAYS B

5-UWR-WEST W-3 DAYS B

5-FWC-EAST W-3 DAYS B

5-FWC-WEST W-3 DAYS B

5-ASW-EAST W-3 DAYS B

5-ASW-WEST W-3 DAYS B

5S-1-EXT MILLED A

SS-1-INT MILLED A

5S-2-EXT MILLED A

5S-2-!NT MILLED A

SS-3-EXT W-3 DAYS B

SS-3-INT W-3 DAYS B

SS-4-EXT W-3 DAYS B

SS-4-INT W-3 DAYS B

916-1-EXT MILLED B

916- 1-INT MILLED B

916-2-EXT MILLED B

916-2-INT MILLED B

916-3-EXT W-3 DAYS c 916-3-INT W-3 DAYS c 916-4-EXT W-3 DAYS c 916-4-INT W-3 DAYS c 6-1-EXT MILLED c 6-1-INT MILLED c 6-2-EXT MILLED c 6-2-INT MILLED c 6-3-EXT MILLED c 6-3-INT MILLED c 6-4-EXT MILLED c 6-4-INT MILLED c

W =Weathered Note: I in. = 25.4 mm; I sq in. = 645 mm2

eral beams used strands that had been exposed to weathering in the casting bed for a few days before the concrete was cast.

The duration of weathering for these strands is indicated in Table 1 under the heading "Strand surface." Table 1 also summarizes the strand configura­tion used in various beam specimens, including the areas of both the top and

January-February 1994

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

2.00 24.25 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

1.75 24.47 4 1.224 0.306

2.00 24.00 4 1.503 0.334

2.00 24.00 4 1.503 0.334

2.00 24.00 4 1.503 0.334

2.00 24.00 4 1.503 0.334

2.00 24.25 4 1.336 0.334

2.00 24.25 4 1.336 0.334

2.00 24.25 4 1.336 0.334

2.00 24.25 4 1.336 0.334

2.00 24.25 4 1.536 0.384

2.00 24.25 4 1.536 0.384

2.00 24.25 4 1.536 0.384

2.00 24.25 4 1.536 0.384

2.00 25.00 3 1.152 0.192

2.00 25.00 3 l.l52 0.192

2.00 25.00 3 1.152 0.192

2.00 25.00 I 3 l.l52 0.192

2.50 25 .00 3 1.302 0.215

2.50 25 .00 3 1.302 0.215

2.50 25.00 3 1.302 0.215

2.50 25.00 3 1.302 0.2 15

2.50 25.00 3 1.302 0.2 15

2.50 25.00 3 1.302 0.215

I

2.50 25.00 3 1.302 0.215

2.50 25.00 3 1.302 0.215

bottom strands, and the distances to the centroids of the top and bottom strands measured from the top of each beam.

A three-part designation is used to identify an end of a beam, as illus­trated by "5S-1-EXT." The first part refers to the diameter of the strands used in a beam where:

5 = !1 in . (13 rnm) strand, nominal

diameter of0.5 in. (12.7 mm) 5S = !1 in. special strand, nominal di­

ameter of 0.5224 in. (13.3 mm) 916 = 'X6 in. (14 mm) strand, nomi­

nal diameter of 0.5625 in. (14.3 rnm)

6 = 0.6 in. (15 rnm) strand, nom­inal diameter of 0 .6 in . (15.2 rnm)

The second part of the designation refers to one of the beams prestressed with the strands , and the third part refers to a specific end of this beam. The INT or EXT refers to the interior or exterior end of a beam as defined in Fig. 4. For the beams from the strand manufacturers ' group, the second part of the designation refers to the name of the manufacturer and the third part refers to an end of the beam.

MATERIALS All prestressing steel used was

seven-wire, low-relaxation strand with a specified ultimate tensile strength of 270 ksi (1860 MPa). Strands of four different sizes supplied by FWC were ~ in . (13 rnm), !1 in. special (13.3 rnm), 'X6 in. (14 rnm), and 0.6 in. (15 rnm) di­ameter strands. Additional Y2 in. ( 13 mm) diameter strands were fur­nished by three other manufacturers : SW AI, UWR and ASW.

Nominal diameter (db) , cross-sec­tional area (Ap,) and pitch of twist of the outer wires of the strands are listed in Table 2. The pitch of twist is the distance along the length of the strand over which a wire of the strand makes a complete revolution.

All shear and confinement rein­forcement used in the bridge girders was of ASTM A-615, Grade 60 rein­forcing steel. The configuration was consistent with current (TDOT) speci­fications . A TDOT mix design for 28-day concrete compressive strength of 5000 psi (34.5 MPa) was used. The concrete mix design is provided in Table 3.

FABRICATION OF SPECIMENS

All test specimens were fabricated by a local producer in accordance with the generally accepted production practices approved by the PCI Plant Certification

73

Table 2. Properties of prestressing strand. Table 3. Concrete mix design.

Area of prestressing Pitch of Quantity Description steel, Aps (sq in.) outer wires (in.) --------------------Strand size I Diameter (in.)

752 lb

1920lb

1326lb

Type I cement (Signal Mountain) ~ in . 0.5

~ in . special 0.5224

I

0.1 53

0.167

7

7 No. 67 coarse aggregate (American Limestone Co.)

Fine aggregate manufactured sand ~6 in. 0.5625

I

0.192 8.38 (American Limestone Co.)

0.6 in. 0.6 0.217

Note: I in. = 25.4 mm; I sq in. = 645 mm2

9 21.2 oz.

35 gal.

Low range pozzolin 300 (Master Builders Inc.)

Water

Note: I lb = 0.454 kg; I oz. = 30 ml ; I gal. = 3.8 I.

Ram Head Load,P

31'-0" Type I AASHTO Beam reinforcement varies)

j, deflection 1 measurement

·''-~

Bearing Block: Structural Tubing 12" X 12" X 1/ 2" L-r~---J

Filled with Concrete

Beam span (30' Typ.) .. To convert from inches to mm, multiply by 25.4. To convert from ft. tom, multiply by 0.305.

Fig. 4. Loading arrangement for development length tests.

Program. Two beams from each of the strand diameter groups were cast simul­taneously, end to end, in a 123 ft 4 in. (37 .6 m) long prestressing bed. The four beams having 1.75 in. (44.5 mrn)

strand spacing were cast individually, each with strands solely from one of the four manufacturers. All strands were initially stressed to a tension of 203 ksi (1400 MPa).

Specimens were steam cured for ap­proximately 16 hours. The transfer of the prestress force was made when the concrete compressive strength reached a minimum of 4000 psi (27.6 MPa) , except for two cases in which the pre­stress was transferred when the com­pressive strengths were 3350 and 3750 psi (23.1 and 25.8 MPa). Transfer of the prestress force was achieved by si­multaneously flame cutting the strands at both ends of each beam, one strand at a time.

INSTRUMENTATION AND TEST PROCEDURE

After all the strands in each beam had been tensioned to 5 kips (22.2 kN) each in the casting bed, electrical resis­tance strain gauges were bonded paral-

74

lei to the longitudinal axis of the heli­cal individual outer wires of the twisted strands to monitor any changes in strain. These gauges were then wa­terproofed and mechanically protected.

The gauges were located from the end of each beam at a distance equal to the estimated development length. Strain readings were zeroed before ad­ditional tensile force was applied to the strands, and the changes in strain were monitored before casting of con­crete, just before and just after pre­stress transfer, and before the static test to failure.

Transfer Length Measurements

Transfer length measurements were made on both ends of each beam using the following method. After the forms were removed, mechanical gauge points were affixed to both sides of the beam, using an appropriate adhesive. Starting from each end of the beam, 15 gauge points were equally spaced at about 4.92 in. (125 mm).

The gauge points were located along the neutral axis (NA) of the beam and along the center of gravity of the steel (CGS). A mechanical strain indicator,

having a nominal gauge length of 9.82 in . (250 mm) and a preci sion of 0.0001 in. (0.0025 mm) was used to measure the precise lengths between the gauge points immediately before and after detensioning of all the strands.

The total deformation on the con­crete surface over a gauge length is the algebraic difference in two respective readings. The average strain is the total deformation divided by the gauge length, and it is assumed to occur at the middle point of the gauge length. The average of the average strains of the corresponding middle points on both sides of the beam was calculated and plotted against the longitudinal di stance of the middle points from the end of the beam. Such a plot of trans­fer length strain di stributions was made for the NA and for the CGS on each end of the beam.

Development Length Tests

Bearing 6 in. (152 mm) at each end onto two supporting steel tubes filled with concrete, all test beams were in­dividually loaded using a hydraulic ram as illustrated in Fig. 4. The dis­placement at the top of each beam at the load point was monitored by a lin­ear variable differential transformer (LVDT).

The displacement measured by the L VDT was used to control the move­ment of the hydraulic ram head. A load cell attached to the ram head monitored the applied force of the ram. Dial gauges were mounted on all the bottom strands at the loaded end of each beam to measure any strand end slippage during the test.

Attempts were made to determine it­eratively the full development length of the beams. Load was applied on a beam at a distance from the end of

PCI JOURNAL

Transfer Beam 6-3-EXT 5oo .--------.--------r-------.--------.

§ ·c (1j 400 ~ .£ Q)~

'0 "' Q

~ -~ 300 1-< ..., u "' Q 0 0 1-<

~~ 200 ................................. ····t······························· . .................................................................... . Q~ I

;a ::s

.j::; bO

A I

.§ 100 ........................ ........ ......... ....................................................................................................

I 23" 68<\, o ~~~~~~~~~~~~~~~~~~~~

0 20 (0.51 m)

40 (1.2 m)

60 (1.53 m)

80 (2.04 m)

Distance from End of Beam (in.)

Fig. 5. Transfer length strain distribution diagram for beams.

beam equal to the estimated full devel­opment length for the type of strands in the beam. If end slip (bond failure) of any of the strands occurred before reaching the ultimate flexural com­pression failure, then subsequent tests of the beams with the same strands were made with the load located at a longer distance from the end of the beam. Conversely, if flexural com­pression failure occurred without any strand slippage, subsequent tests were conducted with the load at a shorter distance from the end of the beam.

TEST RESULTS Considerable experimental data

have been gathered in the UTK test program . At each end of the test beams, a set of measurements of trans­fer length, strand end slip and steel strain was obtained at strand release during the fabrication process, and load vs . deflection and load vs. steel strain relationships were acquired dur­ing the development length test. The ends of strands were gauged during the test and any end slips detected were recorded. The ultimate mode of failure for each test, either shear or flexure, was identified.

Out of the total of 20 full-scale AASHTO Type I prestressed concrete

January-February 1994

bridge beams, 39 development length tests were successfully performed and 40 sets of transfer length strain distri­bution data were obtained. These test results and data are presented in the following subsections, with interpreta­tion of each type of data.

Transfer Length

Fig. 5 presents a typical transfer length concrete strain distribution dia­gram upon prestress transfer. Two subsets of data points are plotted in the figure. Each data point represents the average of the corresponding strain measurements from both side faces of the end of each beam. The subset with the larger strains relates to the data from the CGS, while the one with the smaller strains relates to the data from the NA.

The transfer length is defined as the distance required to transfer the fully effective prestressing force from the strand to the concrete. In other words, transfer length is the length of bond from the free end of the strand to the point where the prestressing force is fully effective. The bond resistance that exists at the ends of a beam im­mediately after prestress transfer is specifically called the transfer bond.

Because multiple layers of strands

were used in the beam, the measured concrete strain was the average effect of the transfer bond of all the strands. Since the concrete strain is linearly proportional to the compressive force at any section for low concrete stress, the average steel stress gradient (or the transfer bond) of the strands can be calculated from the slope of the con­crete strain vs. transfer length curve in Fig. 5.

Ideally, the strains in the concrete would remain nearly constant beyond the transfer length unless the beam is subjected to transverse loadings. The constant concrete strains imply that a horizontal line can be constructed for the portion of the beam beyond the transfer length. Some random devia­tions in the data points from the sup­posedly horizontal portion of the strain distribution diagram are apparent. The deviations are probably due to the nonhomogeneous nature of concrete and the limited precision of the mea­surements. It is reasonable to assume that such random errors also exist within the transfer length, thereby making the reconstruction of the ac­tual concrete strain distribution dia­gram there less definitive.

Careful interpretation of the data points obtained is essential to recon­struct the actual strain distribution dia­gram correctly and determine the transfer length. Previous studies•-6 on the bond characteristics of prestressing strands have consistently demon­strated that the bond behavior of the strands is characterized by small elas­ticity and large plasticity . The bond behavior implies that the transfer bond is mostly constant over the transfer length. Therefore, a straight line fitting the data points can be drawn that makes a constant slope in the transfer length portion of the strain distribution diagram. The intersection of this line with the horizontal line previously drawn as the average strain on the concrete with full effective prestress is approximately the end of the transfer bond zone.

Due to the type of instrument used which measures the average change of strain within a nominal gauge length of 9.82 in. (250 mm), a sharp change in slope of the actual strain distribu­tion diagram near the end of the trans-

75

Table. 4. Summary of transfer length data of specimens.

Elastic shortening Transfer length, L1 Bond

Specimen J:; is; Mechanical Electrical J,. Measured ACIIAASHTO Measured strength -

f.Jt: I designation (psi) I (ksi) D1, (ksi) d1, (ksi) (ksi) in. db --

s8o I 1

5- 1-EXT 3780 203 16.4 18 186 36 72

5- 1-INT 3780 203 550 15.5 18 187 30 60

5-2-EXT 4 170 203 525 14.8 18 188 35 70

5-2-INT 4 170 203 I

520 14.7 18 188 29 58

5-3-EXT 4775 203 450 12.7 - 190 23 46

5-3-fNT 4775 203 420 11.8 - 191 22 44

5-4-EXT 5235 203 390 11 .0 - 192 22 44

5-4-INT 5235 203 390 11.0 - 192 26 52

S-SW AI-EAST 5129 203 340 9.6 II 193 20 40

S-SW AI-WEST 5 129 203 330 9.3 II 193 2 1 42

5-LWR-EAST 5553 203 305

I

8.6 - 194 2 1 42

5-UWR-WEST 5553 203 300 8.5 - 194 19 38

5-FWC-EAST 4775 203 380

I

10.7 - 192 18

I

36

5-FWC-WEST 4775 203 4 15 11 .7 - I9I 18 36

5-ASW-EAST 5 154 203 350 9.9 - 193 2 1 42

5-ASW-WEST 5 154 203 365 10.3 - 192 18 36

SS-1-EXT 5340 203 440 12.2 I3 190 33 63

SS-1- lNT 5340 203 410 11 .4 13 19 1 33 63

SS-2-EXT 4950 203 430 11 .9 I3 19 1 34 65

SS-2-fNT 4950 203 4 15 11 .5 13 19 1 30 57

5S-3-EXT 54IO 203 430 11 .9 12 19 1 3 1 59

5S-3-fNT 54IO 203 455 12.6 I2 190 36 69

5S-4-EXT 5300 203 450 12.5 I2 190 35 67

5S-4-fNT 5300 203 440 1 12.2 I2 190 22 42

9I6-I-EXT 3360 203 680 19.9 18 183 42 75

916- 1-fNT 3360 203 640 18.8 18 184 32 57

916-2-EXT 3750 203 580 17.0 18

I

186 36 64

9 16-2-fNT 3750 203 580 17.0 18 I86 28 50

9 I6-3-EXT 5060 203 390 I 1.4 16 19I 30 53

9 16-3-INT 5060

I

203 390 11.4 16 191 23 4 1

9 16-4-EXT 4950 203 400 11 .7 16 191 30 53

916-4-fNT 4950 203 390 11 .4 16 191 27 48

6- I-EXT 4 100 I 203 450 12.6 I9

I

190 25 42

6-1-fNT 4 100 203 450 12.6 19 190 27 45

6-2-EXT 4280 203

I

490 13.7 19 189 30 so

6-2-fNT 4280 203 490 13.7 19 189 24 40

6-3-EXT 5230 203 430 12.0 12 19 1 23 38

6-3-fNT 5230 203 405 11.3 12 I9 1 2 I 35

6-4-EXT

I

5450 203 450 12.6 12 190 22 37

6-4-fNT 5450 203 425 11 .9 12 19 1 23 38

Note: I psi= 6.89 kPa; I ksi = 6.89 MPa; I kip= 4.445 kN; I in. = 25.4 rnm.

fer length gives the average strain measurements there that appear to fit a transitionally smooth curve. The point right at the end of the transfer length has the maximum concrete strain equal to that beyond the transfer bond zone, but the measured average strain over the gauge length centered at the

76

point would be less than the maxi ­mum. Failure to recognize this fact can lead to the identification of trans­fer lengths from the same data that, on second look, appear to be too large.

The method of data interpretation just presented, which might be termed a "slope-intercept" method, is a rea-

db ACIIAASHTO V1 (kips/in.)

62.0 1.1 6 0.79 1

62.3 0.96 0.954

62.6 1.12 0.820

62.6 0.93 0.99 1

63.3 0.73 1.263

63.6 0.69 1.326

63.8 0.69 1.332

63.8 0.8 1 1.127

64.3 0.62 1.476

64.4 0.65 1.408

64.6 0.65 1.4 13

64.7 0.59 1.563

63.9 0.56 1.630

63.6 0.57 1.622

64.2 0.65 1.403

64.1 0.56 1.634

63.4 1.00 0.963

63 .7 0.99 0.967

63.5 1.02 0.936

63.7 0.90 I .063

63.5 0.93 I .027

63.3 1.09 0.88 1

63.3 1.06 0.907

63.4 0.66 1.445

60.9 1.23 0.835

6 1.2 0.93 1.1 02

6 1.8 1.04 0.989

6 1.8 0.8 1 I .272

63.7 0.84 1.223

63.7 0.64 1.595

63.6 0.84 1.22 1

63.7 0.75 1.359

63.3 0.66 I .634

63.3 0.7 1 1.513

62.9 0.79 1.353

62.9 0.64 1.692

63.5 0.60 1.78I

63.7 0.55 1.958

63.3 0.58 1.856

63.5 0.60 1.782

sonable and consistent method for de­termining the length required to trans­fer steel stress to concrete. However, when the results are finally translated to a design equation for transfer length, a multiplier greater than unity may need to be applied to ensure a conservative design.

PCI JOURNAL

fu Table 5. Development length test results of specimens. ::l c Ill

-< ..;., CD r::r 2 Ill

-<

Specimen ~~ Lood ,~,~ s ..... ....... designation (psi) Lp (in.) location Lg (in.)

- . - - -

5- 1-EXT 5476 92 92

S- 1-INT 5476 69.6 69.6

5-2-EXT 6746 77.4 77.4

S-2- lNT 6746 I

85 58

5-3-EXT 6858 85. 1 93

5-3-lNT 6858 77.4 8 1

5-4-EXT 7600 8 1.25 67

5-4-INT 7600 77.4 86

5-SW AI-EAST 5553 8 1 84

5-SWAJ-WEST 5553 69.6 87 5-UWR-EAST 5989 77.4 -

5-UWR-WEST (S) 5989 69.6 -

5-FWC-EAST 534 1 72.5 -

5-FWC-WEST 5341 77.4 -

5-ASW-EAST 5400 73.5 -

5-ASW-WEST _ 5400 -f-- 69.6 -

SS- 1-EXT 6624 69 1 69

5S- I-INT (LC) 6624 8 1 50 SS-2-EXT - 84 90

SS-2- INT (S) 6800 82.5 82.5

SS-3-EXT 5967 8 1 66 5S-3-lNT 5967 75 75

SS-4-EXT 6 18 1 68 66 5S-4-lNT 6 18 1 72 Ill

9 16- 1-EXT 5533 106 106

9 16- 1-INT 5533 87 87 9 16-2-EXT 592 1 96 65

9 16-2-INT 592 1 87 87

9 16-3-EXT 6 11 9 95.5 11 4 9 16-3-INT 6 11 9 104.4 105

9 16-4-EXT 6237 104.4 87.5

9 16-4-lNT (LC) 6237 108 95.5

6- 1-EXT 5 126 11 6 11 6

6- 1-INT(S) 5 126 93 66

6-2-EXT 5285 83.5 83.5

6-2-INT 5285 74.4 92

6-3-EXT 7463 83.52 85 .5

6-3- INT 7463

I

88. 16 93

6-4-EXT

I

7984 85.84 89 6-4- lNT 7984 85.84 95.5

Ultimate load

Pu (kips)

11 4.0

125 .0

124.0

120.0

127.0

138.0

132.0

135.0

125.3

147 .0

138.0

177.0

137.5

134.0

134.3

142.0

127.0

142.0

-16 1.0

125.0

122.0

130.0

144.0

110.0

130.0

11 4.0

126.0

114.0

109.0

108.0

108.0

99.0

155.0

126.0

138.0

134.0

129.0

I

130.0

1:n o

Note: 1 in . = 25.4 mm; 1 kip = 4.445 kN; 1 kip-ft = 1.36 kN-m; 1 ksi = 6.895 MPa.

Mode of

fa ilure

B-F

B-S

B-S

B-F

I

F

B-F

F

B-F

F

F-B

B-F

B-F

B-F

F

F

F

B-S

F-B -

F-B

F-B

B-S

B-S

B-F

B-F

B-F

B-F

B-F

B-F

F

B-F

F

F

F

B-F

B-F

B-F

F

F

F

Maximum shear Moment (ki p-ft) f se f sb f su fsm Load at stra nd slippage

Vu (kips) M er Mb Mu (ksi) (ksi) (ksi) (ksi) Load (kips) [Strand No.] (Fig. 3)

9 1.2 396 61 1 645 19 1 259 265

I

268 108[ 1] ; 11 0[6,7,8,9] 107.0 469 550 564 19 1 234 240 - 122[ I ,6,7,8,9] 104.0 444 6 12 6 12 19 1 259 259 262 124[ I ,3,5,7,8,91 98. 1 4 15 623 639 19 1 234 242 257 11 7[5,7,8,9]

103.0 388 - 675 19 1 - - - No slip 11 5.0 408 645 679 19 1 262 265 270 13 1[7,8] ; 135[9]; 1381 1,3.5 1

109.0 4 10 - 676 19 1 260 260 - No slip

11 2.0 453 644 664 19 1 n/a - - 13 l ln/al 104.0 430 - 64 1 200 - 269 273 No slip

125.0 485 660 660 200 269 270 274 147fn/a l 11 5.0 463 630 679 - - - - 128[n/aj

134.0 459 6 11 707 - - - - 153[n/a]

11 7.0 4 19 624 640 -

I

- -

I

- 134[n/a l 11 2.0 448 - 660 - - - - No sli p

11 4.0 429 - 633 - - - - No sli p 12 1.0 463 - 638 - r ,;, - - No sl ip -109.0 466 565

I

569 199 232 - 126[4]

11 7.0 449 7 19 724 199 2 17 2 17 - 14 1[7,8,9]; 138.5[4]

- - - - 199 - -100.0 408 692 692 199

I

260 260

I

- 16 1 [n/a]

103.0 47 1 - 640 200 - 253 26 1 125[ I ,4,6,7,8,9] 103.0 457 587 587 200 245 245 - 122[1 ,4,6,7,8,9 1 11 2.0 442 530 574 200 24 1 243 - 120[1] ; 130151 122 .0 472 601 666 200 24 1 255 - 130[5] ; 14417,R,] --83.9 488 682 688 185 240 240 248 109[7,8] 105.0 476 633 703 185 222 242 258 11 7[1] ; 12217,8] 90.0 455 642 665 185 2 10 - - 11 0[7,8,9]; 11 214,6 1; 11 411 ,3] 102 .0 465 677 682 185 n/a 203 - 125[ I ,3,4,6,8,9 J 90. 1 4 19 628 663 187 220 2 18 - 95[7]; 108[8 1; 11 0[91; 11 314 ] 83.7 390 - 675 187 - - - No sli p

82.9 390 60 1 669 187 222 246 248 97 [n/a]

8 1.9 4?9 - 688 187 - 25 1 - I Noslip 73.2 4 12 1 - 658 184 232 - - [ No slip 95 .3 335 - 682 184 2 17 - - No slip 103.0 398 660 660 184 232 - 126[n/a j

116.0

I

462 609 657 184 226 244 - 128 [ n/a]

11 0.0 424 696 70 1 19 1 n/a - - 133[n/a] 104.0 426

I

- 704 19 1 - 268 - No slip

106.0 406 - I 695 19 1 -I 262

- No slip

108.0 428 - 7 11 19 1 - 265 - No slip

(675 kN) Load Versus Deflection for Beam 5-3-EXT 150~------~--------~--------r--------,

Cor$pression Fail I

(450 kN)

j ~ I

i (I)

0.. 100 ........................ f···························· .... ..f:~?..~~i.P. ............. . :i2 -o' ol

3

(225 kN) so

0.5 (12.7 mm)

I ! I !

I

1.0 (25.4 mm)

Deflection, in.

1.5 2.0 (38.1 mm) (50.1! mm)

Fig. 6. Typcial flexural compression failure (F).

(950 kN) Load Versus Deflection for Beam 6-2-Int 200~-------r------~--------~------~

(675 kN) 150

(225 k~6 ---

0.5 1.0 1.5 2.0 (12.7 mm) (25.4 mm) (38.1 mm) (50.8 mm)

Deflection, in.

Fig. 7. Typical slip and flexural compression failure (B-F).

Table 4 lists the concrete strength at transfer, !;;. the specified initial pre­stress, f si• elastic shortening (ES) as measured from the change in strain on the concrete surface of each specimen in the unit of rnicrostrains (J.Lc) and the corresponding steel stress loss, D15, the effective prestress, fse• and the transfer length, L,, obtained immediately after transfer according to the slope-inter­cept method. The f se is obtained by subtracting the D15 from the fs;·

78

For comparison with the measured transfer length, Table 4 also lists the transfer length calculated as fs e/3 times the nominal diameter of the strand. The term Cfse /3)D is not specif­ically identified in the AASHTO Specifications or ACI Code, but it is a part of the AASHTO and ACI devel­opment length equations. The effec­tive prestress multiplied by the area of an individual strand gives the effective prestress force in the strand. The aver-

age transfer bond strength, U,, is cal­culated by dividing the effective pre­stress force in the strand by the trans­fer length.

Development Length Tests

The development length test results for all the beams are summarized and presented in Table 5. For each test, these data are tabulated: the concrete strength at the time of test, J;, the point from the nearer end of the beam where load is applied, LP' the location of the electrical strain gauges from the end of the beam, L

8, the maximum mea­

sured load, P11, and the corresponding shear force, Vu, the mode of failure of the beam, and the measured flexural moments at the load point and steel stresses at the gauge point at different important stages during the test.

The effective prestress at the time of test was determined from readings of electrical resistance gauges. The val­ues listed in Table 5 are not perfectly consistent with those in Table 4 , which were obtained using a mechani­cal strain gauge.

The flexural moments at the load point are calculated from the measured applied load on each beam with the as­sumption of simple supports at the beam ends. The cracking moment, Me, is , on the average, about 66 per­cent of the ultimate moment, Mu. The moment at which the first strand slip­page is detected, Mb, is also calculated and tabulated for beams with bond failure.

The effective prestress, f se• in the strands was measured with electrical strain gauges just before each develop­ment length test. Listed in Table 5 are the observed steel stresses at the gauge point at first slippage of the strands, fsb• and at the maximum applied load, f su• during the development length tests. Some higher steel stresses in the strands were also observed in a few of the beams when the beams were de­flected beyond their ultimate loads and plastic hinges were forming beneath the load points. These maximum steel stresses observed are tabulated as f sm·

Due to a malfunction in the con­troller of the hydraulic loading equip­ment, data on the very first develop­ment length test were not acquired. Of

PCI JOURNAL

the 39 development length tests per­formed , end slip was not detected in 13 tests, four showed "slight" end slips after flexural compression fail­ures were developed, 17 experienced end slips but did eventually fail in flexural compression, and five exhib­ited shear fail ure immediately after a bond failure .

Beam Behavior and Mode of Failure

The behavior of the test beams can be generally categorized into four dif­ferent modes of failure, which are ex­plained briefly here with reference to the typical load vs. deflection plot. The load vs . deflection plot for each test can be found in the final project report. 2

Fig. 6 shows a typical load vs . de­flection plot for a flexural failure de­noted in Table 5 by "F." This plot is for Test 5-3-EXT. The beam exhibited linear behavior up to cracking; then the stiffness rapidly decreased with in­creasing deflection and, ultimately , concrete crushing occurred at the max­imum moment. The failure is typical of a beam with adequate development length and, thus , without any strand slippage.

Typical load vs. deflection plots for tests with bond failure are shown in Figs. 7 and 8. Beams showed the typi­cal linear behavior up to cracking load and then nonlinear behavior until a bond failure, indicated by end slip, occurred. The bond failure occurred prematurely, before the ultimate flexu­ral strength. Losses in bond were sub­sequently accompanied by premature flexural compression failure or shear failure, denoted as "B-F" or "B-S ," respectively.

When a bond failure is detected only at loads very near to the flexural compression failure or just after the compressed concrete fiber begins to crush, the beam is evidently loaded at a point very close to the full develop­ment length. This mode of failure is denoted as "F-B ," and a typical load vs. deflection plot for this is shown in Fig. 9.

Stress increase in the steel above the effective prestress is relatively small up to cracking of the section . These

January-February 1994

(675 kN) Load Versus Deflection for Beam 5-1-INT 1so~-------r-------.--------·~ -------.

! Sli ' p I ~

I shear Failure

I (225 kN)+--~IIIf-t-----l----t-----1 so

o ~~~~~~~~~~~~~~~~~~

0.0 0.2 (5.1 mm)

0.4 (10.2 mm)

Deflection, in.

0.6 (15.3 mm)

0.8 (20.4 mm)

Fig. 8. Typical slip and shear fai lure (8-S).

(900 kN) Load Vs. Deflection for Beam SS-1-INT 200

(675 kN 150

"' 0. ~ 'ti ell

.3

(225 kN

! Flexural jCompres'·; sion

Fjillure , ! E1~-·· -r-

i ~ f !

--·-----·-+------·-·~·----·~·--- L-----i ; ; ! l l l I i i , I i l l

so -r -1 - -- r- --O f"~~~~~~~~~~~~~~~~~

0.0 0.5 1.0 1.5 2.0 2.5 3.0 (25.4 mm) (50.8 mm) (76.2 mm)

Deflection, in.

Fig. 9. Typical flexural compression and slip failure (F-8).

DISCUSSION OF TEST RESULTS

stress ranges, however, are typical of service conditions; service loads in pretensioned slabs and beams are usu­ally below the cracking loads. As indi­cated by the strain gauges, steel strains below the load point increased abruptly at the initial flexural crack and continued to increase until failure of the beam occurred. A measured load vs. steel strain, plotted in Fig. 10, clearly illustrates this behavior.

The res ults of the development length tests are discussed at some length herein in the section where those results are presented. Develop­ment length consists of transfer length plus flexural bond length and is re­lated to the overall beam behavior.

Development length is difficult to

79

~ :.;;l

120

(445 kN 100

)

(356 kN 80

).

-g .3 (267 kN)

60

(178 kN) 40

(89 kN 20

0

)

0

io--"'""' ..... ,..._ i&.

~ ~

.., , v I

BF: Strand #1

/ Flexural Co pression Fai lure

iFirs Flexural Cr ck BF: Stu d #6,7,8,9

1000 2000 3000 4000 5000

Change in steel strain during test, microstrains

Fig. 10. Load vs. steel strain for Beam Test 5-1-EXT, Strand 3.

80~----------------------------------~

El 70

Ill

60 • •

50

40

Ill

~ fsi/3

-~----

•

II high Lt/db

• mean Lt/db

11 low Ltldb

El

•

30+-~~--~-r~~~~--r-~-.--~,-~~

0.48 0.50 0.52 (12.7 mm)

0.54 0.56 0.58 0.60 0.62 (15.24mm)

Fig. 11. Plot of transfer length in terms of strand diameter for different strand sizes.

Table. 6. Average transfer lengths of beams.

Average transfer length, db - -

Strand Milled Weather 1-day Weather 3-day

)4 in . 64.5 46.5 39.0

)4 in. special 62.2 - 59.3

Y,, in. 62.2 - 48.9

0.6 in. 40.6 - -

Note: I in. = 25.4 mm.

80

measure precisely and the variables af­fecting it are difficult to quantify. On the other hand, transfer length is much easier to quantify. In the following sections some of the variables that af­fect transfer length are discussed. All conclusions are based on tests of strands in mill condition unless other­wise noted.

Effects of Strand Diameter

The perimeter of seven-wire pre­stressing strand is approximately equal to 4/3ndb. Adhesion force, which is directly proportional to the amount of adhered surface, is therefore directly proportional to the strand diameter. Friction may be affected by strand di­ameter due to the difference in normal force from different wire sizes. Be­cause the grooves between the outer wires of a strand get larger with in­creasing strand diameter, mechanical bond strength would tend to increase with strand diameter.

Table 4 and Fig. 11 illustrate that the average transfer lengths for the ~ in. (13 mm), ~ in. special (13.3 mm) and % in. (14 mm) strands of milled surface condition are approximately proportional to the strand diameter, but this relationship does not hold for the 0.6 in . (15 mm) strand s . The shorter transfer length for 0 .6 in . (15 mm) strands may be attributed to the increase in mechanical bond.

Effects of Strand Surface Condition

The wires of all stress-relieved and low-relaxation strands have residual surface lubricants , usually stearates, resulting from the wire drawing pro­cess. These residuals result in less ad­hesion between the concrete paste and the wire than would be provided by clean, bare wire. Weathering, which is not sufficient to create visible rust, causes microscopic roughness which considerably improves bond . From Table 6, the average improvement in the transfer length for one-day weath­ering of ~ in. (13 mm) diameter strand was about 27.9 percent, while that for three-day weathering of the same strand appears to be about 40 percent.

This reduction in transfer length is due to increased adhesion of the con-

PCI JOURNAL

crete and an increased coefficient of friction between the concrete and the strand. Because the strands of all man­ufacturers were in the group that weathered, no definite conclusions can be drawn as to relative bond character­istics of the different strands in the milled condition.

Transfer Length

The method used to determine the transfer length from measured data is described herein and referred to as the slope-intercept method. It is the opin­ion of the authors that the slope-inter­cept method best represents the data obtained during the research and that it is logically based on the mechanical strain gauge method of determining transfer length.

Based on this interpretation of the data from the transfer length tests, the conclusion is drawn that, consistent with ACI and AASHTO, the length re­quired to transfer a particular steel stress to concrete is approximately equal to the stress in ksi divided by three and multiplied by the diameter of the strand in inches. As the stress being transferred initially is isi• a reasonable expression for calculating transfer length is L1 = UsJ3)db. This equation is consistent with the test results and is somewhat more conservative than the ACI and AASHTO requirements.

The plot in Fig. 11, which shows mean transfer lengths as well as upper and lower transfer lengths measured in the tests, clearly demonstrates that calculating L1 as one-third the stress at transfer times the bar diameter is rea­sonable and conservative for the ~in., ~ in. special and %6 in. (13, 13.3 and 14 mrn) strand sizes. As noted earlier, the transfer length for 0.6 in. (15 mrn) diameter strand is somewhat less than for the other sizes.

Development Length

The development length data ob­tained from the static tests to failure lead to the conclusion that the ACI and AASHTO provisions for calculat­ing development length are somewhat unconservative. The development length equation given by these two codes is in the following form:

January-February 1994

The right-hand side of the equation can be split into two parts:

in which the first term, Usel3)db, rep­resents the transfer length and the sec­ond term, Ups - ise) db, represents the flexural bond length.

The other symbols are:

Ld = development (in.)

ips = stress in prestressed reinforce­ment at nominal strength (ksi)

ise = effective stress in prestress­ing steel after losses (ksi)

db = nominal diameter of pre­stressed reinforcement (in.)

The results of a number of research efforts, including the work reported herein, were reviewed by Chew 10 in terms of the flexural bond strength ob­tained. He found that the flexural bond strength, which appeared to be justi­fied by tests, is approximately 42 per­cent higher than the value implied by the ACI and AASHTO equations. In other words, the flexural bond length required by the code equations is ap­proximately 42 percent lower than that justified by the tests.

Consistent with Chew's findings and with the earlier discussion on transfer length, the following equation for development length is proposed:

The proposed equation increases the calculated development length ( 1) through increasing the transfer length portion of the equation by using is; rather than ise• and (2) through multi­plying the flexural bond length portion by 1.5. For a case with is; = 180 ksi (1240 MPa), ise = 160 ksi (1100 MPa) and ips = 260 ksi (1790 MPa), Ld in­creases from 153.3 db to 210 db, a 37 percent increase.

Obtaining accurate values of devel­opment length from tests is not a well­defined, straightforward procedure. While the equation just presented gives values of development length which compare reasonably well with the data presented in Table 5, further work to refine this prediction is clearly necessary.

FHWA Memorandum

Since the October 26, 1988, FHWA memorandum created the need for this research, it is appropriate to formulate comments on the various restrictions imposed by the subject memo. The data obtained during this research sup­ports the following conclusions:

1. The use of 0.6 in. (15 mrn) diam­eter strands should not be prohibited. In fact, 0.6 in. (15 mm) diameter strands have shorter transfer lengths in relation to their diameters than any of the other three sizes tested. The mea­sured development lengths were com­parable to the other strand sizes, and the ultimate moments were substan­tially higher than those predicted by either the ACI or AASHTO equations.

2. Based on these data, the authors see no need to restrict the use of 0.6 in. (15 mrn) diameter seven-wire pre­stressing strand.2 Spacings of less than four times the diameter were only tested using ~ in. (13 mm) diameter strand. As the authors understand it, this is a fairly common practice for West Coast manufacturers of pre­stressed concrete beams. Eight test beams were constructed with strand spacings of 1.75 in. (44.5 mrn). There was no significant difference between the moment capacities of beams with this spacing and those with 2.0 in. (51 mm) spacing, and in every case the measured moment capacity was at least 10 percent greater than that pre­dicted by ACI and AASHTO.

The beams with 1.75 in. (44.5 mrn) spacing were the beams with weath­ered strands, a condition quite likely to occur in practice. In view of the excel­lent performance of these beams, with no observed splitting, there appears to be no valid reason not to use this spac­ing. Based on these data and the fact that extensive field use has produced no adverse effects, it is recommended that the spacing requirement for ~ in. ( 13 mm) diameter prestressing strand be reduced to 3.5 strand diameters.

3. Increasing the development length for all strand sizes to 1.6 times the value obtained from the AASHTO equation is not justified. The authors would recom­mend the equation proposed under the discussion on development lengths, which would result in an increase of about 35 percent for most cases.

81

4. This research did not investigate the effects of debonding; therefore, no conclusions can be drawn relative to this restriction.

RECOMMENDATIONS The following recommendations are

based on the research presented in this paper:

1. The transfer length for ~ in., ~ in. special and %6 in. (13, 13.3 and 14 mm) strand sizes should be calculated as:

2. Further work should be done to de­velop an expression for transfer length of 0.6 in. (15 mm) diameter strand. In the meantime, the equation recom­mended for other strand sizes, which is clearly conservative, may be used.

1. Cousins, T. E., Johnston, D. W., and Zia, P., "Transfer and Development Length of Epoxy Coated and Un­coated Prestressing Strand," PCI JOURNAL, V. 35, No. 4, July­August 1990, pp. 92-103.

2. Deatherage, J. H., and Burdette, E. G., "Development Length and Lateral Spacing Requirements of Prestressing Strand for Prestressed Concrete Bridge Products," Final Report sub­mitted to the Precast/Prestressed Con­crete Institute, The University of Ten­nessee, Knoxville, TN, September 1991.

3. Janney, J. R., "Nature of Bond in Pre­Tensioned Prestressed Concrete,"

82

3. The use of 0.6 in. (15 mm) diam­eter strand should be accepted as stan­dard practice.

4. A center-to-center spacing of 1.75 in. ( 44.5 mm) should be permitted for ~in. (13 mm) diameter strands.

5. The development length of all strand sizes should be calculated as:

ACKNOWLEDGMENT The research that is reported herein

was performed under the sponsorship of the Precast/Prestressed Concrete Institute and the Southeast Trans­portation Center, the US DOT's Re­gional University Transportation Cen­ters Program. Their financial support of the work and their timely review

REFERENCES

ACI Journal, V. 50, No.9, May 1954, pp. 717-736.

4. Hanson, N. W., and Kaar, P. H., "Flexural Bond Tests of Preten­sioned Prestressed Beams," ACI Journal, V. 55, No. 7, January 1959, pp. 783-803.

5. Janney, J. R., "Report of Stress Trans­fer Length Studies on 270K Prestress­ing Strand," PCI JOURNAL, V. 8, No. 1, February 1963, pp. 41-45.

6. Over, R. S., and Au, T., "Prestress Transfer Bond of Pretensioned Strands in Concrete," ACI Journal, V. 62, No. 11, November 1965, pp. 1451-1460.

7. Zia, P., and Mostafa, T., "Develop-

and constructive criticism of the final report are gratefully acknowledged.

Ross Prestressed Concrete in Knoxville built the prestressed con­crete beams that were tested and thus played a key role in the research. Their special efforts and flexible coop­eration are much appreciated.

A number of graduate students and post-doctoral research faculty played key roles in the research effort and are deserving of mention and thanks. Most notable of these are Brian Smith, Ken Griffin, Bud Cheatham, Jeff Wilkinson, and Francis Oluokun.

Any opinions, findings, conclu­sions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the Precast/Prestressed Con­crete Institute.

ment Length of Prestressing Strand," PCI JOURNAL, V. 22, No. 5, September-October 1977, pp. 54-65.

8. Preston, H. K., "Bond of Seven-Wire Strand," Technical Bulletin, Wiss, Janney, Elstner Associates, Inc., Princeton Junction, NJ, 1988.

9. Smith, B. R., "An Investigation of the Variables Affecting the Transfer Length of Prestressed Concrete Mem­bers," M. S. Thesis, The University of Tennessee, Knoxville, TN, December 1989.

10. Chew, Chong Key, "Development Length of Prestressing Strand," Ph.D. Dissertation, The University of Ten­nessee, Knoxville, TN, May 1991.

PCI JOURNAL

Aps = area of prestressed reinforce­ment

Cv = distance from bottom of member to neutral axis

Dfs = loss of prestress due to elastic shortening (mechanical gauge)

dfs = loss of prestress due to elastic shortening (electrical gauge)

CGS = center of gravity of strand

db = nominal diameter of pre­stressing strand

Es = modulus of elasticity of steel

fJ = concrete compressive strength at time of test

fci = concrete compressive strength at transfer of prestress

January-February 1994

APPENDIX- NOTATION

ips = steel stress at nominal beam strength

fsb = stress in strand at bond slip

fsu = stress in strand at ultimate moment

fse = effective stress in prestressing steel after losses

fs; = initial prestress in steel rein­forcement

fsm = maximum stress in strand measured during test

I = moment of inertia of beam section

Lb = flexural bond length of strand

Ld = development length of strand

Lg = distance of electrical strain gauges from end of beam

L1 = transfer length of strand

LP = distance of load point from nearest end of beam

Mb = moment at bond failure

Mer = cracking moment of section

Mu = ultimate moment capacity of section

NA = neutral axis of beam

P u = maximum measured load

ut = average transfer bond length

Vu = maximum shear force

)1£ = elastic shortening, microstrains

83